JND models in pixel domain directly calculate the JND at pixel level with considerations of either/both luminance adaption (LA) or/and contrast masking (CM) effects of the HVS. As the pioneering work, Chou et al. [1]} first proposed a spatial-domain JND model by combining LA and CM. Afterwards, Yang et al. [2]} further proposed a generalized spatial JND model with a nonlinear additivity model for masking effects (NAMM) to characterize the possible overlaps between LA and CM. Based on Yang et al.'s work, Liu et al. [3]} introduced an enhanced pixel-level JND model with an improved scheme for CM estimation. Specifically, the image is first decomposed into structural component (i.e., cartoon like, piecewise smooth regions with sharp edges) and textural component using a total-variation algorithm. Then, the structural and textural components are used estimating EM and TM effects, respectively. In order to differently manipulate order and disorder regions, Wu et al. [4]} designed a novel JND estimation model based on the free-energy principle. An autoregressive model is first applied to predict the order and disorder contents of an input image, then different schemes are used to estimate the JND threshold of these two parts, respectively. Further, Wu et al. [5]} took the concept of pattern complexity (PC) into account for JND estimation. They quantified the pattern complexity as the diversity of pixel orientations. Finally, pattern masking is deduced and combined with the traditional CM for JND estimation. Jakhetiya et al. [6]} further combines RMS contrast with LA and CM to build a more comprehensive JND model in low-frequency regions. For high-frequency regions, a feedback mechanism is used to efficiently mitigate the over- and under-estimations of CM. Chen et al. [7]} took horizontal-vertical anisotropy and vertical-meridian asymmetry into consideration to yield a better JND estimation. The basic consideration is that the effect of eccentricity on visual sensitivity is not homogeneous across the visual field. Shen et al. [8]} decompose the image into three components namely luminance, contrast, and structure. Since the masking of structure visibility (SM) is unknown, they trained a deep learning-based structural degradation estimation model to approximate SM. Finally, LA, CM and SM are combined to estimate the overall JND. Wang et al. [9]} proposed a novel JND estimation model by exploiting the hierarchical predictive coding theory. They simulated both the positive and negative perception effects of each stage individually and integrated them with Yang's NAMM model [2]} to yield the total JND threshold.
